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Complex Numbers

by Robert Waltz

Rated: 18+ · Book · Personal · #1196512

Not for the faint of art.

Complex Numbers

A complex number is expressed in the standard form a + bi, where a and b are real numbers and i is defined by i^2 = -1 (that is, i is the square root of -1). For example, 3 + 2i is a complex number.

The bi term is often referred to as an imaginary number (though this may be misleading, as it is no more "imaginary" than the symbolic abstractions we know as the "real" numbers). Thus, every complex number has a real part, a, and an imaginary part, bi.

Complex numbers are often represented on a graph known as the "complex plane," where the horizontal axis represents the infinity of real numbers, and the vertical axis represents the infinity of imaginary numbers. Thus, each complex number has a unique representation on the complex plane: some closer to real; others, more imaginary. If a = b, the number is equal parts real and imaginary.

Very simple transformations applied to numbers in the complex plane can lead to fractal structures of enormous intricacy and astonishing beauty.

http://www.ddewey.net/mandelbrot/

Signature for Honorable Mentions in 2018 Quill Awards

A signature for exclusive use of winners at the 2019 Quill Awards

Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

tj-turkey-jobble-jobble-hard-J

about 17 hours ago
In response to "Revisited: "A Frank Discussion""

I became disgruntled with meat sold in local grocery stores; half the weight is water, the taste is bland, and it's "use by" date is usually one day away. I found a small town butcher/locker plant that sells locally raised meats and buy in bulk so it's actually fresher, cheaper, and better tasting. Recently, I decided to try my hand at making our own sausage as well. It's a bit of work, but I think it's worth the trouble.

1 Like

Turkey DrumStik

a day ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

Write_Mikey_Write!

Nov 14, 2024 at 2:04pm
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

Nov 14, 2024 at 12:10pm
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

1 Like

June 27, 2023 at 10:01am

#1051660

Jeté

Wrapping up my entries for June's "Journalistic Intentions"

[18+]...

jeté

(This time, I added the accent aigu myself.)

Long ago, I took a cinema class in college. I might have mentioned this before. No, it doesn't make me an expert on movies or anything; it was mostly an easy B and a different movie to watch every week.

One film that stuck in my head was an artsy French science fiction short called La Jetée. While the words "artsy" and "science fiction" may give some readers pause, it can work. It's also more of a slide show than a "movie," but that's part of the art.

The basic thrust (that's a pun, but you might not know it yet) of the film is that a kid witnesses a death on a jetée (which is the French name for the observation platform of an airport, and yes, it's related to the English "jetty").

Later, after the apocalypse, the guy's sent back into time and (spoiler alert) dies on the jetée, realizing at the end that he was the man whose death he'd witnessed in his youth.

Does that sound familiar? It should. A few years later, when 12 Monkeys came out, I remember watching it and thinking, "I really hope Gilliam acknowledges La Jetée for this idea." And, indeed, he did.

Of course, that synopsis fails to capture the metaphorical breadth and depth of the original film. It really is worth watching, and now that I know more French, I might even try to find a version without English subtitles.

As a verb, the french "jeter" means to throw. The dance term, "jeté," has a meaning closer to thrust (also, it's a past tense construction); hence the really very obscure pun above. Because one doesn't really throw a leg (unless it's a prosthetic); one thrusts it. "Jetée" is a related word (feminine gender) for a structure that's thrust out into something else, like the abovementioned observation platform, or how a jetty is kind of thrust into the ocean.

You can see I'm avoiding the more obvious, salacious puns related to gender and thrusting. Why? Not because they're salacious, but because they're too obvious for a professional punster such as myself.

What I really want to know, though, is this: starting maybe about 15 years ago, a neologism entered the English language. I despise most neologisms, but this one is inherently funny. The word is "yeet," and it's a verb meaning something like "to throw without concern." As in "I watched him yeet the ball right through the asshole's window, then walk away." What I'm wondering is if it's inspired by the French jeter— as the "j" sound sometimes does become a "y" in linguistics.

There's also some confusion over whether the past tense is "yeeted" or "yote," and I'm rooting for the latter.

4 Like • Comment • View 2 comments

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